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APPROXIMATION OF AND BY COMPLETELY MONOTONE FUNCTIONS

Part of: Approximations and expansions Integral transforms, operational calculus Foundations, constitutive equations, rheology

Published online by Cambridge University Press:  06 March 2020

R. J. LOY Open the ORCID record for R. J. LOY [Opens in a new window]  and
R. S. ANDERSSEN Open the ORCID record for R. S. ANDERSSEN [Opens in a new window]
R. J. LOY*
Affiliation:
Mathematical Sciences Institute, Hanna Neumann Building No. 145, Australian National University, CanberraACT 2601, Australia email rick.loy@anu.edu.au
R. S. ANDERSSEN
Affiliation:
Data61, CSIRO, GPO Box 1700, Canberra, ACT 2601, Australia email Bob.Anderssen@Data61.CSIRO.au
*
✉rick.loy@anu.edu.au
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Abstract

We investigate convergence in the cone of completely monotone functions. Particular attention is paid to the approximation of and by exponentials and stretched exponentials. The need for such an analysis is a consequence of the fact that although stretched exponentials can be approximated by sums of exponentials, exponentials cannot in general be approximated by sums of stretched exponentials.

Keywords

complete and absolute monotonicitystretched exponentialapproximationcompletely monotone and Kohlrausch functionsuniform and pointwise convergence

MSC classification

Primary: 41A30: Approximation by other special function classes
Secondary: 41A10: Approximation by polynomials 44A10: Laplace transform 76A10: Viscoelastic fluids
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 4 , October 2019 , pp. 416 - 430
Copyright
© 2020 Australian Mathematical Society

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